The integration of Artificial Intelligence (AI) into Integrated Development Environments (IDEs) is reshaping software development, fundamentally altering how developers interact with their tools. This shift marks the emergence of Human-AI Experience in Integrated Development Environment (in-IDE HAX), a field that explores the evolving dynamics of Human-Computer Interaction in AI-assisted coding environments. Despite rapid adoption, research on in-IDE HAX remains fragmented which highlights the need for a unified overview of current practices, challenges, and opportunities. To provide a structured overview of existing research, we conduct a systematic literature review of 89 studies, summarizing current findings and outlining areas for further investigation. Our findings reveal that AI-assisted coding enhances developer productivity but also introduces challenges, such as verification overhead, automation bias, and over-reliance, particularly among novice developers. Furthermore, concerns about code correctness, security, and maintainability highlight the urgent need for explainability, verification mechanisms, and adaptive user control. Although recent advances have driven the field forward, significant research gaps remain, including a lack of longitudinal studies, personalization strategies, and AI governance frameworks. This review provides a foundation for advancing in-IDE HAX research and offers guidance for responsibly integrating AI into software development.